Is there any evidence in the suttas showing the Buddha was "flexible" in his teaching of Dhamma? Or do the suttas show the Buddha wished his teachings to remain consistent & clearly representative of what he taught?
I think the Buddha explained Dhamma, and that the explanation was adapted according to who he was addressing.
This footnote to the Sigalovada sutta, for example, suggests that "worshipping the six directions" was a Vedic ritual, and the Buddha takes advantage of the occasion to teach a different doctrine.
But that's not to say that the doctrine is incompatible with the doctrine taught in other suttas (but it is rather different to the Rhinoceros sutta for example).
Or according to Piya Tan the Aggañña Sutta (DN 27) is addressed to Brahmins (i.e. probationary monks who were Brahmins) and is perhaps a parody of Brahminical creation myths. The subject matter is "fantastic" but the doctrine (i.e. that the fall is due to craving "nourishment") is again not incompatible with other suttas.
I don't mean to generalise about the whole Digha Nikaya. But you ask whether he was "flexible, or, wished to remain consistent" -- perhaps he was flexible 'and' remained consistent.
I think that's famously part of his ability as Buddha, i.e. to know how to teach different people.
One of the suttas which shows that "the Buddha wished his teachings to remain consistent & clearly representative of what he taught" is (perhaps ironically, given the question) the Maha-parinibbana Sutta i.e. DN 16 -- which includes the "four great references" and so on.
Incidentally in this answer Bonn says ...
I can answer the question if I still quote the original text from Tipitaka and Atthakatha without making them conflict with each other.
I never try to make Tipitaka conflict with each other, never make Atthakathā conflict with each other, and never cut any part of Tipitaka and Atthakathā off.
... and in this answer ...
People who can understand the noble truth from tipitaka must can deconflict every uncleared word of tipitaka
... so I presume it's possible that, I think it's the opinion of e.g. Thai/Buddhist scholars that, the teachings are consistent.
In my opinion though (I don't know about Bonn's) to say "they're consistent" might need some flexibility (and good-will, and if not 'faith' exactly then at least a willingness to listen) in how you interpret them -- words have a range of meanings, they're often used metaphorically, part of the doctrine is not being over-attached to specific views, I think they are adapted/suited to the specific audience (often a reply to a specific question), etc.
Perhaps my opinion (above) is overly rosy though, and there are bits (of suttas) -- not all in the Digha Nikaya -- which I overlook or ignore. I don't think I'd want to argue the doctrinal details you identify in your answer -- some of your comments (e.g. about namarupa) I just don't understand or have no opinion about; and some (e.g. about DN 27) isn't how I read that sutta (and I'm content with my reading of it but I'm not sure it would benefit anyone to try to argue about it with you).